International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
Performance Evaluation of MMSE and LS
Channel Estimation in OFDM System
1
2
Ajay Bahadur Singh1, Vivek Kumar Gupta
Department of Electronics & Communication Engineering, DIT, Dehradun, India
Assistant Professor,, Department of Electronics & Communication Engineering, DIT, Dehradun, India
Abstract— Since from last two decade Orthogonal
Frequency Division Multiplexing (OFDM) got lots
interest in mobile communication systems. In OFDM
system, the radio channels which we use are frequency
selective and vary with time for wireless wideband
mobile communication system. The transfer function of
these radio channels is unequal in time as well as in
frequency domain, due to which a dynamic estimation
of these channels should required at the demodulation
point of OFDM. In this research work, we use Pilotaided Least Square (LS) and Minimum Mean- Square
Error (MMSE) estimator for estimating the channel of
OFDM system with different modulation techniques i.e.
16-PSK, 4-QAM, 8-QAM,16-QAM. In simulation, we
compare the performance of both estimators with
proposed modulation schemes, which results that LS
has preferred performance with low complexity while
MMSE has best performance with one drawback i.e. it
has high complexity.
Keywords--OFMD, Communication Channel, MMSE,
LS, PSK, and QAM.
nature of the radio channels used in OFDM system,
channel estimation is required before the modulation
of OFDM [1].
OFDM enables simple equalization of
frequency selective finite impulse response (FIR)
channels. It is the blessing of the Inverse fast Fourier
Transform (IFFT) pre-coding and Cyclic Prefix (CP)
of having length greater than that of the length of
channel memory at the transmitter end. In each block
the CP consists of redundant symbols before the
IFFT. At the transmitter the combination of IFFT and
CP with FFT at receiver converts the frequency
selective channels into parallel flat faded subchannels, each one with different sub-carriers. These
flat fades can be removed by dividing each subchannel output with channel attenuation at the
prospective sub-carrier.
Current and future broadband wireless
communication systems aim to provide high data rate
services. As a result, multipath fading becomes a
major concern as systems with high data rate are
more liable to inter symbol interference (ISI) due to
the increase in the normalized delay spread. It is
hence interesting to use modulation schemes that
were robust to multipath fading. Orthogonal
Frequency Division Multiplexing (OFDM), because
of the division of a high rate data stream into a
parallel of lower rate data streams, provides the much
needed resistance to multipath fading and has
attracted increasing interest in past decade.
In OFDM system, the estimation channel
can be done either by adding pilot tones with all
symbols having specific period. The two basic
technique used for estimating the channel are Block
type pilot channel and comb type pilot channel
estimation, in which the pilots are inserted in
frequency and time direction respectively. LS is used
to arrange the block type pilot based scheme under
the assumption that the channel is slow faded, while
the transfer function of channel is considered as
stationary for OFDM data. The transfer function of
previous channel is used as the transfer function of
present channel. Practically, the channel transfer
function of a wideband radio channel may have
significant changes even within one OFDM block.
Hence, the channel estimation is required at every
block of the OFDM symbol.
Due to the some characteristics of OFDM
i.e. high data rate transmission, high bandwidth
efficiency and its robustness to multipath delay, it is
applied to the wireless communication systems.
OFDM is also used in the wireless LAN standards
and in multimedia wireless services i.e. Japanese
Multimedia Mobile Access Communication. Due to
the frequency selective nature and time varying
Firstly, the features of OFDM system are
introduced including modulation based on Fast
Fourier Transform (FFT), the system structure of
OFDM and its mechanism used to counteract
frequency-selective fading. In this research work we
compare the LS and MMSE under the influence of
different modulation techniques in MATLAB
emulator.
I.INDRODUCTION
ISSN: 2231-5381
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
Fig.1 Baseband OFDM system
II. SYSTEM DESCRIPTION
The pilot based channel estimation based
OFDM system is shown in fig.1. The binary
information is firstly grouped according to
modulation in ‘’signal mapper.’’ After adding pilots
either to all sub-carriers with specific time period
between the information data sequence. IDFT block
in base band OFDM system is used to transform the
data sequence of length { ( )} into time domain
signal { ( )}with the following equations:
s(v)  IDFT{U ( x)}
v=0,1,2,…….,L-1
L 1
  U ( x )e j ( 2xv / L )
( )is Additive White Gaussian Noise
Where,
(AWGN) and ℎ( )is the channel impulse response.
The channel response ℎ can be represented by [2]
0 ≤
r 1
≤
−1
h(v)  hie j (2 / L) fDiTv  (  i )
i 0
Where, is the total number of propagation
paths, ℎ is the complex impulse response of the ℎ
path,
is the ℎ path Doppler frequency shift, ʎ is
the delay spread index, T is the sample period and
is the ℎ path delay normalized by the sampling
time. At the receiver, after passing to the discrete
domain through A/D and low pass filter, guard time
is removed:
x 0
( )
Where, L is DFT length. Following IDFT
block, guard time, which is chosen to be larger than
the expected delay spread, is inserted to prevent intersymbol interference. This guard time includes the
cyclically extended part of OFDM symbol in order to
eliminate inter-carrier interference (ICI). The
resultant OFDM symbol is given as follows:
( )=
( + ), = − , − + 1, … . , −1
( ), = 0, 1, … … , − 1
Where,
is the length of the guard interval.
The transmitted signal ( ) will pass through the
frequency selective time varying fading channel with
additive noise. The received signal is given by:
( )=
( ) ⊗ ℎ( ) + ( )
ISSN: 2231-5381
( )=
−
+
≤
≤
−1
, = 0,1, … . . − 1
Then ( )is sent to DFT block for the
following operation:
( )=
{ ( )} = 0, 1, 2 … . − 1

1 L 1
y (v )e  j ( 2xv / L )

L v 0
Let us considered that there is no ISI [3],
shows the relation of the resulting Y(x) to H(x) =
DFT {h(v)}, I(x) that is ICI because of Doppler
frequency and W(x) = DFT {w(v)}, with the
following equation [4]:
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
( ) = ( ) ( )+ ( )+
( )
=
,
= 0, 1 … . − 1
Following DFT block, the pilot signals are extracted
( ) for the data suband the estimated channel
channel is obtained in channel estimation block. Then
the transmitted data is estimated by:
)
+ (
,
Where,
is
LS
estimate
of
channel
,
condition at the pilot position,
is variance of
noise,
is a matrix having transmitted pilot on its
diagonal, and
is channel autocorrelation
matrix which is given by
=
=
( )
= 0,1, … − 1
( )
Then the binary information data is obtained
back in ‘’signal demapper’’ block.
The different types of channel estimators considered
in our research work. After channel estimation
process at pilot subcarrier position, the channel
responses at the rest of data sub-carrier are estimated
by interpolation. Firstly, interpolation at time domain
which has two symbols time spacing. In our research
work we use linear interpolation for time domain
interpolation because it is sufficient for small time
spacing.
III.1. LS Channel Estimation
In the simple case, the channel estimates, are
found by straight forward multiplying the received
pilot by the inverse of known transmitted pilot. This
method is also known as Least Square (LS) estimator,
[5]:
=
=
(1)
(1)
(2)
…
(2)
(
(
)
)
Without using any knowledge of statistics of
the channels. The LS Estimator has very low
complexity, but they suffer from a high mean-square
error.
III.2. MMSE Channel Estimation
The MMSE channel estimator obeys the
second order statistics of channel condition to
minimize the mean-square error the major drawback
of MMSE estimator is its high complexity, which
grow exponentially with observative samples. The
frequency domain MMSE estimate of channel
response is given as [6]
ISSN: 2231-5381
∗}
{
III. CHANNEL ESTIMATION
,
For this given case, the correlation function
between channel frequency response values is given
as [7]
1,
(
)/
1−
( − )/
2
=
≠
From above equation we get
MMSE
interpolation for all sub-carrier can be performing by
modifying the MMSE estimator at equation to get all
data sub-carrier’s channel responses.
=
+
=
(
)
,
,
The MMSE estimator uses a known
knowledge of
and
, and is optimal when
these statistics of channel are known. The values of
SNR are predefined: higher target SNRs are easy to
obtain more accurate estimates. The robustness
estimator design requires account for worst
correlation of multipath channel, namely when
channel power-delay profile (PDP) is uniform in
nature [8].
IV. SIMULATION AND EXPERIMENT
This section, tells about the performance of
channel estimation by LS and MMSE for OFDM
system under the influence of different modulation
techniques, in the terms of channel MMSE
and ⁄ . For simulation we set length of IFFT to
64 and length of cyclic prefix (CP) is 8.
In our research work and simulation result
we compare the performance of LS in frequency
domain and MMSE in frequency and time domain. In
fig.2 we use 4-QAM with the bit of per symbol is 2.
In fig.3 we use 8-QAM having bit per symbol is 3. In
fig.4 we are using 16-QAM with the bit per symbol is
4. In fig.5 we are using 8-PSK with the bit per
symbol 3 and in fig.6 we are using 16-PSK with the
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
bit per symbol equal to 4. Fig.2-fig.6 is shown below
in perspective order.
Fig.4. Channel estimation by LS and MMSE using 16QAM
Fig.2.Channel estimation by LS and MMSE using 4-QAM
Fig.5. Channel estimation by LS and MMSE using 8-PSK
Fig.3. Channel estimation by LS and MMSE using 8-QAM.
Fig..6. Channel estimation by LS and MMSE
using16-PSK
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 1 – Sep 2014
VI. CONCLUSION
The result of our research work that, mean
square error is continuously improved as the SNR
increases to its maximum value i.e. 40 dB. When we
compare the LS and MMSE in terms of mean square
error later one gives better performance than former.
Furthermore, MMSE works much better in frequency
domain than time domain at the higher value of SNR.
When we use, 16-QAM as a modulation technique in
OFDM system the channel estimation result is very
much improved in comparison of 4-QAM, 8-QAM,
8-PSK, and 16-PSK.
ACKNOWLEDGEMENT
It was my great pleasure in extending
special thanks to Mr. Vivek Kumar Gupta, and my
elder brother Mr. Vijay Bahadur Singh under whose
guidance and help, I was able to propose my work in
the form of this research paper. I’ am deeply
inhibited to themselves for their training and
guidance throughout my work. They was always
been a source of constant inspiration and
encouragement for me.
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BIOGRAPHY
Ajay
Bahadur
Singh
presently lives in Dehradun
and
completed
his
Graduation as a B. Tech.
graduate in the field of
Electronics
and
communication from Uttar
Pradesh
Technical
University, Lucknow, UP, India in 2010. He is a
post-graduate scholar in the field of Wireless &
Mobile Communications from Dehradun Institute
of Technology, Dehradun, Uttarakhand, India in
2013. Presently he is working on “Channel
Estimation for OFDM system”. He became the
member of IJETT
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